BxMO 2012 Problem 2

Answer

Find all quadruples $(a, b, c, d)$ of positive real numbers such that $a b c d=1$ , $a^{2012}+2012 b=2012 c+d^{2012}$ and $2012 a+b^{2012}=c^{2012}+2012 d$ .

Dataset text NuminaMath olympiads. Quoted with source.

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(a, b, c, d)=\left(t, \frac{1}{t}, \frac{1}{t}, t\right) \text{ for any } t>0

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